Electrical properties of thin metallic films

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Ames Laboratory ISC Technical Reports Ames Laboratory

3-20-1952

Electrical properties of thin metallic films

D. B. Barker

Iowa State College

W. C. Caldwell

Iowa State College

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Electrical properties of thin metallic films

Abstract

The Hall coefficient and conductivity of silver films were measured by a DC method and comparisons with the theoretical calculations of Fuchs and Sondheimer were made. Films from 150 A. to 1500 A. in thickness were deposited by evaporation at pressures below 10^-2 microns. The electrical properties were studied at liquid nitrogen, dry ice and acetone, and room temperatures. Film thickness measurements were made by the interferometer method. Electron diffraction and electron micrograph pictures were taken to study agregation and to check on the purity of the films. The electron micrographs show aggregation in films less than 300 A. thick. The electrical measurements also indicate this change in the thinnest films. A variation of Hall coefficient and conductivity with thickness was found but only qualitative agreement between theory and experiment was indicated.

Keywords

Ames Laboratory

Disciplines

Other Physics | Physics

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ATOMIC

ELECTRICAL PROPERTIES

OF THIN METALLIC

FILMS

By

D

.

B. Barker

W

.

C

.

Caldwell

March 20, 1952

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PHYSICS

Reproduced dire(!t from copy a.s submitted to this office.

PRll'JTE.D IN USA PRICE 2Cl CENTS A.vailab:i.e fran;. the Office of Technical Services

Department of Commerce Wash.2ngton 25~ D. C.

Work performed under Contract No. 'w-740)-eng-82.

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ELECTRICAL PROPERTIES OF THIN METALLIC FILMS

BY

D. B. Barker and W. C~ Caldwell

ABSTRACT

The Hall coefficient and conductivity of silver films were measured by a DC method and comparisons with the theoretical

calculations of Fuchs and Sondheimer were made& Films from

150 A. to 1500 A. in thickness were deposited by evaporation at

pressures below lo-2 microns~ The electrical properties were

studied at liquid nitrogen, d~ ice and acetone, and room

temperatures~ Film thickness measurements were made by the

interferometer method~ Electron diffraction and electron

micro-graph pictures were taken to study agregation and to check on

the purity of the films. The electron micrographs show

aggre-gation in films less than 300 Ao thick.. The electrical

measure-ments also indicate this change in the thinnest filmso A variation of Hall coefficient and conductivity with thickness

was found but only qualitative agreement between theory and

experiment was indicatedo

INTRODUCTION

Theoretical calculations of the electrical characteristics of bulk

metals are made3 in the simplest case~ in terms of the free electron

theory (1). The calculations are essentially classical9 assumine only

from the quantum approach that the electron energies are proportional to

the square of the wave vector, kj and that these energies are distributed

according to Fermi-Dirac statistics~ The conduction electrons are assumed

free to migrate with thermal energy through the lattice.? undergoing collis-.

ions much as molecules in a gaso The effects of the collisions at the

surface of the solid are assumed to be negligible compared to those within.

The average distance of el.e ctron travel between collisions is defined as

the mean free path~

If any dimension of a metallic conductor approaches in magnitude the

mean free path lengthj as is possible in evaporated films, surface effects

must be consideredo Fuchs (2) has made an analysis of this condition for

the case of plane films with an electric field applied parallel to the

critical surfaces. His calculation was similar

w

that performed for

bulk materials except that new boundary conditions were applied for the

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ISC-215

For the simplest case9 Fuchs assumed that all electrons striking the

surfaces vmre scattered diffusely 1d th a complete loss of their drift velocities. The resulting equations were solved numerically in terms of the ratio of the bulk metal conductivity,

a-

,

to the thin film conducti-vity, cr and the ratio of the film thicknesg_, a, to the mean free path length,JL e A graphical presentation of the solution is shown in

Fig~

1.

Fuchs obtained a more complete roJution by ~ing a p:n-ameter~ E. , Wlich represented the fraction of the electrons that reflected specularly at the surface. As £ approaches one, the curve in Fig. 1 approaches a horizontal line corresponding to a conductivity ratio of unity.

Sondheimer (3) has extended this analysis for the case of a magnetic f:i.eld perpendicuJa r to both the critical surface and the electric field., The same assumptions were made and the methods of solutions similaro For low magnetic fields (up to 15 or 20 kilogauss) Sondheimer0 s solutions for the conductivity ratios agreed with those obtained by Fuchso At high

fields he found that the conductivity oscillates as the field is increasedQ SondheimerVs solution for the ratio of the thin film Hall coefficient, A~ to the bulk metal coefficient3 ~o.? with diffuse reflection of the electrons and low magnetic fields, is shown in Figo 2. His parameter p, has the same significance as €9 as p approaches one,:~ this curve also drops to a value of unity.

Since the electronic mean free path for even the best conductors is _about

500

A., very thin films are necessary to study these effects. Such

films may be prepared by chemical deposition, sputtering.., or evaporation .. Of these three processes, evaporation is the simplest and most rapid.

A few films of gold were deposited for an initial investigation, but the principal study has been made with silvero Silver is easily evaporated, is not highly active chemically, has a large electronic mean free path, and has bulk. conductivity· properties in agreement with calculations. based on the free electron theory. These characteristics make silver a particularly suitable metal for studying thin filmsc

EVAPORATION OF FILMS

Glass microscope slides were used as substrates for the films.· Just before use~ these were carefully cleaned in Dichromate cleaning solution and then with Dreft suds in distilled water~ They were rinsed with several hundred milliliters of boiling distilled water from a wash bottle and

allowed to dry in a dust free atmosphere~ All handling was done with forceps.

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THEORETICAL CURVE (FUCHS € = 0 )

-+

EXPERIMENTAL CURVES

FOR FILM SERIES 130 140

AT ROOM TEMPERATURE - -

-+-

--o---AND LIQUID NITROGEN

TEMP._e--ct--\ ~

+

"'-~

(t(t

\

\o o, \

~'

'

o'o

'

' ...

... ~ ...

0-.5 2

y-

5

FIG. I. ELECTRICAL CONDUCTIVITY OF THIN SILVER FILMS.

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1.8

1.7

1.6

1.5

AH 1.4

AH0 1.3 1.2 1.1 1.0. 1 ..._<» ct .2

+

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FIG.2

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THEORETICAL

(SONDHEIMER P= 0)

SERIES 130 14 0

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HALL COEFFICIENTSOF THIN SILVER FILMS.

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Current

.-r---

contact

Silver film

~-- Gloss slide

Conductivity probe placed

here. ---t--1;:~ _ _.

a.

~

Fig. 3. Arrangement of ailver film on glau alide.

r---tllljt---'\if'W\1'\/V---,

Wet Cell

A-Thermocouple

8-Voltage drop for

conductivity. C-Hall voltage

0-Volta~e drop for

cur rent value.

..

Rheoatat

0.1 ohm Standard Reaiator

~ Selector

,.

Switch

Potentiometer Galv.

Ff~. 4. Circuit far electrical meaauremenh.

Ma~netlc field perpendicular to plane of film.

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A filament was constructed

qy

winding approximately two feet of 0.010

in. diameter~ 98~% purity, Makepeace~ silver 1dre on a 6 or 7 turn~ 0.3 ine

diameter, tungsten helix of 0~030 in~ diameter wire., A coil of 0.008 in. diameter molybdenum wire was loosely wound over the silver. When the

silver melted~ surface tension caused it to form membranes stretched bebreen the tungsten and molybdenum wL res~ The filament was thus able to

hold a greater charge of silver and more surface area was provided for

evaporation.

After the filament and shielded substrates had been loaded into the

vacuum chamber and a vacuum of about 100 microns had been attained~ a gas discharge of 70 rna. at about 3000 volts was maintained for 15 mine to further clean the substrates by ion bombardment~

When the. vacuum had reached 1 micron a shutter was swung between the filament and the substrates

qy

moving a magnet outside the bell jar. Then

the filament was heated just above the melting point of silver for

5

to 10 sec. to prefuse the silver and outgas the filament structure~

Following this~ the system was allowed to pump for 10 to 12 hours to allow further outgassing. At the end of this time the vacuum was below

the minimum gauge readings lo-2 microns, The shutter was then opened

and the films deposited by heating the filament to the evaporation point for 10 sec. or less.)) depending on the film thicknes.ses desired., During 2

,this heating the gauge continued to indicate a pressure of less than

10-microns.

Three sets of films including thicknesses from 150 to 1)00 A. were

prepared by this method and labeled series 130, 140, and 150. The films

were stored in a dessicator at normal pressures and temperatures except

while measurements were being madee

ELECTRICAL MEASUREMENTS

All electrical measurements were made with the simple DC potentiometer circuit shown in Fig.

4.

A Rubicon, Type B Potentiometer was used with a

Rubicon~ lamp enclosed type galvanometer having a sensitivity of 0.02 microam:ps & per mm9

For the measurements, the substrate was mounted on a small masonite

board,Which had been sprayed with plastic for waterproofingo Current

contact with the film was made through flat, phosphor-bronze clips and connections for Hall voltage and conductivity were made with spring-brass wire clips. It was found necessa~ to place several layers of aluminum

foil between each clip and the evaporated silver contacts to attain a

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9 ISC-2l5

also provided excellent contact at room temperature but tended to flake off When the assembly was cooled~

The electrical measurements were made in two stages~

First~ a film was mounted in the holder and the assembly placed

in the magnetic fieldo A current of 0~01 ampso to 0.2 amps. was allowed to flow for several minutes to insure that a stable condition existede No heating of the film was ever detectedo Readings were then taken of the voltage drop across the film, the voltage drop across

the standard resistor, and the Hall voltage. The Hall voltage

measure-ment was repeated with the magnetic field reversedo Three sets of

data were taken with the order of the readings varied in order to

eliminate any residual voltage drift effectso The film and holder were then immersed in liquid nitrogen contained in a dewar located

between the poles of the magnet and the series of measurements repeated at this temperatureo After being removed from the liquid

nitrogen, the sample was warmed to room temperature and the condensed

moisture evaporated off by a small blotver., The room temperature measurements were repeated to check for any irreversible effects of

the cooling.,

After being stored in a dessicator for a period of time from one

to three weeks9 the film was remounted in the holder and carried through a similar process with the liquid nitrogen being replaced by

a dry ice and acetone mixtureo · A polyethylene bag was used to protect

the film and holder from the destructive effect of the acetone. Since

the Hall coefficient changes only Slightly between room and dry ice

temperatures the Hall measurements were not repeatedo

Later, several of the films were mounted in the holder at room

temper-ature, measured, dismounted, and then the cycle repeated several times to

check the reproducibility of the measurementso

FILM THICKNESS MEASURE:MENTS

After all electrical measurements had been completed the thickness of

each film was measured by the interferometer method that has been adequately

discussed and described by Tolansky

(4).

The step in the film was produced by making a scratch with the sharp corner of a microscope slide. This

produced a sharp break in the film without damaging the substrate.b

Some evidence was obtained to indicate that errors can be introduced into the thickness measurements if the top layer of silver is more than

800 or 900 A. thicko This problem should be studied furthero

The equipment used here for these measurements has been described by

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ELECTRON DIFFRACTION AND MICROSCOPY

A study of some of the chemical and physical properties of the thinner films was undertaken to check the continuity and purity of the films.

Samples for study were obtained by placing on each substrate several nickel,

electron-microscope screens covered with a thin collodian filmo Sennett

and Scott (6) have indicated that the physical character of deposited

films is the same for all smooth~ amorphous substrates so a film on

collodian will reveal the nature of the film on glass. The covered screens

were examined in an RCA~

EMU

Electron Microscope which could be used for

either microscopy or diffraction.

EXPERIMENTAL RESULTS ·

The electron microscope screens were examined immediately following the deposition of the films 11 after several ••eeks aging, and after immersion

in liquid nitrogen~ The diffraction studies revealed a small amount of

impurity which has been tentatively identified as

wo

3 in the films of series

130 but none in the films of the other serieso This is presumably due to

the fact that the tungsten filament was maintained at a higher temperature anQ for a longer period of time for the series 130 evaporation than for

the others~

The electron micrographs of the films were similar to those of Sennett

and Scott. Aggregation was evident in films below 200 A • in thickness,

although enough contact ~vas maintained between the individual particles to

allow films as thin as 1~0 A, to conduct. The particles'of the films thinner

than l50A., were about lOOA. 1.n diameter.

No changes were noticed in the films after aging or immersion in liquid nitrogen. The effects of immersion on films deposited on collodian

and on glass are probably different however because of the differences in

the expansion coefficientso

Summaries of the results of the electrical measurements are shown

plotted in Figs.

5 and

6.

The thickness of each film was measured to within

3%

or less. At any one time the electrical measurements could be

reproduced to within 2%. Over the period of aging and i1nmersion some

values changed as much as

5%

11 however no trends predominated in the changes

of the Hall coefficients or the conductivities; some varied monotonica~

up or down~ some randomly~ and some not at allo

The values for the resistivity of bulk silver shovm in Fig.

5

were taken from The Handbook of Chemist~ and Physics (7)o The values for the

Hall coefficient of the bulk material in Table I were averaged from those

given in The International Critical Tables (8).. In Table I are given the

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THICKNESS

SERIES {

215-130 221---+

226---v

234--.

+

+-r

246--+

SERIES

140

8ULK SILVER +

-50 100 150 200 250 300

Temperature (°K)

FIG. 5. TEMPERATURE DEPENDENCE OF RESISTIVITY OF THIN SILVER FILMS

1-' 1-'

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( )

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TABLE I

Electrical Constants for Bulk Silver

Temperature (°K) 77 19.5 29.5

Po

(ohm-em) o38(lo-6) L02.(lo-6 ) 1 .. 60(10-6)

AHo (

c~

/coulomb) .92.(10-4) ,.BB(lo-4) o84(lo-4)

!....{..

/ (cm2/volt-sec) 240 86

53

n

(electrons/c~)

6.,8 (lo22) 7" 1.( lo22 ) 7o4(lo22 ) nl/3 (1/cm) 4ol (10

7)

4~l(lo

7

)

4o2(107)

,~e. (Angstroms) 4.50 710 2000

It is int~resting to note that for the linear portion of the curves in Fig. 6, the change in Hall coefficient with temperature is nearly the same as for bulk materials and that the change is independent of thicknesse If the Sondheimer prediction were true, one would expect the change to be larger for the thinner films~

The sharp break in the region of 300 A~ in the curves which show conductivity or Hall effect as a function of thickness is probably due to aggregation causing a physical change in the filmse In this region the data are a function of the contact between particles as well as the

properties of the particles themselves. A project is now being planned in which films will be deposited on substrates at liquid nitrogen temper-atures and maintained at that temperature while electrical measurements are made ..

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SERIES 130 140 150

ROOM TEMP.--+----o----~-­

LIOUID NITROGEN

TEMP.-·--~---~~~

\•':;·\,

0 '

',

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~---.---~-';,-.o __________ <.._ -o-2..o ____ - - - -

-~-:!---~-~ -~-:!---~-~

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200 400 600 800 1000 1200 1400 1600

Thickness, a, (A)

FIG. 6. HALL COEFFICIENTS OF THIN SILVER FILMS.

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ISC-215'

REFERENCES

1.. Seitz9 F~ The Modern Theory of Solids. N.Y~, HcGraw-Hill Book Co.,

Inc. 1940.- - .

2., Fuchs, K& Proc., Camb. Phil. Soc.

1!±.,

100 (1938).

J,. Sondheimer~ E. H. Phys. ·Rev.

§2.,

401 (19.50).

4

..

Tolansky, S. Multiple-Beam Interferome!:.!z. Oxford, The Clarendon Press. 1948.

5.

Bearinger, V. W. ~ Comparison of Methods of Measurin~ the Thiclmess of Thin Metal Films, Unpublished Ph.D. Thesis.- Ames, Io-vm, Iowa · Stateeollege·"Library. 19.50.,

6

e

Sennett, R. So and Scott, G.D. J. Opt •. Soc.Am.

1±£,

203 (195'0)

o

7. Handbook of Chemistry and Physics. 27th Edo Cleveland, Chemical Rubber Publishing Co~ 1943o

8~ International Critical-Tables of Numerical Data, Physics, Chemistry, and Technolo~~ New York, McGraw-Hill Book Co~, Inco 1929.

Figure

FIG. I. ELECTRICAL CONDUCTIVITY OF THIN SILVER FILMS.
FIG. I. ELECTRICAL CONDUCTIVITY OF THIN SILVER FILMS. p.7
Fig. 3.
Fig. 3. p.9
FIG. 5. TEMPERATURE
FIG. 5. TEMPERATURE p.13
TABLE !2 Constants I for

TABLE !2

Constants I for p.14
FIG. 6.
FIG. 6. p.15